I think I have it figured out. When the taped up guy is handed the deck of cards, his partner has nicked the chosen one or somehow otherwise communicated to the taped up guy which one it is. He shuffles and deals out the 12, which of course the wrong card. When his partner slaps him in the head (and that is the key to the trick), he quickly and almost unseen, slips the chosen card under the tape and into his mouth.